Incollection,
Condition of existence of the supersolid state
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Since Kim and Chan performed the torsional oscillator experiment on solid
Helium 41, the studies on supersolid has been activated. Supersolid state
is characterized by coexistence of diagonal-long-range-order(DLRO) and
off-diagonal-long-range-order(ODLRO), which corresponds to solid order
and superfluid order, respectively.
Theoretically, Matsuda and Tsuneto first proposed hardcore bose Hubbard
model as describing this system2, which can be mapped onto XXZ-model
for spin 1/2 system. And Batrouni showed numerically that supersolid state
is unstable when only nearest-neighbor interaction is considered, but
stable when next-nearest-neighbor interaction is added3. On the other hand, Sengupta examined
softcore bose Hubbard model4, in which two or more particles can exist on
a site, and found stable supersolid phase for densities larger than 1/2.
Supersolid state is understood as a state, in which additional particles form
the superfluid state on the background checkerboard structure.
The Hamiltonian for this system is described by
eqnarray*
H=-t\sum_<ij>(a_i^\daggera_j+a_i a_j^\dagger)+V\sum_<ij>n_i n_j+\\
+U2 \sum_i n_i(n_i-1) -\sum_i n_i
eqnarray*
Here, $t$ is the hopping term between nearest neighbor sites, and $V$ and
$U$ represents the nearest-neighbor and on-site repulsion, respectively.
In this study, we analyze the softcore bose Hubbard model from three
viewpoints below. First, we show that $U$ plays an important role in
realization of the supersolid phase. Also, when we plot the superfluid
order parameter as a function of $U$Fig.1, the curve shows a characteristic
peek structure, which corresponds to the flatness of the effective potential
that additional particles feel.
Second, we examine the lattice dependence on the stability of supersolid
state. Especially, we found the supersolid state on the cubic lattice, and
the dimensionality effect on supersolidity will be discussed. Finally,
we show the meanfield phase diagram of softcore model, and the
correspondence of the phase diagram by meanfield theory and that by
simulation will be discussed.
We use stochastic series expansion scheme in simulations.
1 E.Kim and M.H.W.Chan, Nature. 427, 225 (2004)
2 Matsuda and Tsuneto, Suppl. Prog. Theo. Phys. 46, 411 (1970)
3 G.G.Batrouni and R.T.Scalettar, Phys. Rev. Lett. 84, 1599 (2000)
4 P. Sengupta et.al., Phys. Rev. Lett. 94, 207202 (2005)
